The element‐free Galerkin method for a quasistatic contact problem with the Tresca friction in elastic materials. Issue 1 (29th August 2020)

• Record Type: Journal Article
• Authors: Ding, Rui; Shen, Quan; Huo, Yuebin
• Is Part Of: Numerical methods for partial differential equations. Volume 37:Issue 1(2021)
• Page Start: 69
• Page End: 97
• Publication Date: 2020-08-29
• Subjects: duality algorithm -- element‐free Galerkin method -- moving least‐squares approximation -- penalty method; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22519
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract: This paper is proposed for the error estimates of the element‐free Galerkin method for a quasistatic contact problem with the Tresca friction. The penalty method is used to impose the clamped boundary conditions. The duality algorithm is also given to deal with the non‐differentiable term in the quasistatic contact problem with the Tresca friction. The error estimates indicate that the convergence order is dependent on the nodal spacing, the time step, the largest degree of basis functions in the moving least‐squares approximation, and the penalty factor. Numerical examples demonstrate the effectiveness of the element‐free Galerkin method and verify the theoretical analysis.